1. Field of the Invention
The present invention relates to wireless communication systems and specifically to channel estimation in an orthogonal frequency division multiplexing system.
2. Discussion of Related Art
Digital multimedia applications are becoming more common as the increase in broadband communication systems continues. While the use of broadband wireless communication develops, a prevailing problem in most digital communication systems includes how to determine the original signal (block of symbols) transmitted when a noisy signal is received. One method, called Orthogonal Frequency Division Multiplexing (OFDM), enables the transmission of symbols at high data rates over hostile channels at a relatively low complexity. The OFDM standard has been adopted in some regions, such as Europe, for radio and TV. The standard is being explored in other contexts such as fixed wireless systems. As with other digital communication protocols, OFDM signals experience the same difficulty in being interpreted at a receiver.
Various channels are presently available for digital communications. These include telephone channels, data channels, broadband channels, satellite channels and fixed wireless channels. There is non-uniformity in the characteristics and bandwidth of these channels and such non-uniformity causes inter-symbol interference that inhibits faster transmission. For example, in applications such as broadband channels and fixed wireless channels, a standard problem increasing the complexity of the system is multi-path channels caused by signals reflected off buildings or other objects between the transmitter and receiver. Multiple versions of the same signal interfere with each other and cause inter-symbol interference (ISI) with an accompanying lower bit rate. It becomes difficult to extract the original information from the channel with the presence of ISI.
In order for an OFDM system to recognize transmitted signals, the receiver and transmitter must be synchronized. This synchronization involves several tasks. First, timing synchronization involves finding the “beginning” of a received OFDM symbol. The time scales of the transmitter and receiver are synchronized and any extra symbols repeated in the block to preserve orthogonality can be removed with the required accuracy. Second, frequency synchronization is necessary to estimate and compensate to for any frequency deviation in the radio carrier frequency assigned to modulate the signal. Third, sampling-clock synchronization provides a conversion of the signal produced by a fast Fourier transform (FFT) of the analog signal into an analog signal assumed to be a certain span of time between two values. Last, if a coherent modulation scheme is used, the channel transfer function Hl,k must be estimated and compensated for.
The present invention is most concerned with the channel estimation and compensation process to preserve synchronization in OFDM systems. Channel estimators have been developed with the general purpose of using algorithms to estimate received data sequences at a wireless receiver. The goal of these channel estimators is to produce a computationally and commercially feasible maximum-likelihood (ML) parameter group reflective of the originally transmitted information.
With each block of received data at a receiver, there is unwanted noise that must be taken into account. The process of determining the subject matter on a particular channel may become so computationally complex that various solutions become infeasible. To decrease the complexity, expectation-maximum (EM) algorithms were developed that introduced an iterative process that under some circumstances produce maximum-likelihood parameter estimates. Recovery of transmitted data may be accomplished using such estimates.
One such method for estimating a channel is discussed in “Sequence Estimation in the Presence of Random Parameters Via the EM Algorithm,” by Costas N. Georghiades and Jae Choong Han (IEEE Transaction on Communications, Vol. 45, No. 3, March 1997, pp. 300-304). The contents of this paper are incorporated herein by reference. In the Georghiades et al. paper, the authors teach about an EM algorithm wherein optimizing sequence estimates involves two steps: (1) computing the likelihood function; and (2) maximizing over the set of all admissible sequences. The EM algorithm makes use of a log-likelihood function for the complete data in a two-step iterative procedure that converges to the ML estimation.
Georghiades et al. provide several examples of applying the EM algorithm. They discuss the application of the algorithm to the random phase channel in Section III and the fading channel in Section IV. Georghiades et al. explain that with respect to the fading channel, they propose applying the EM algorithm to address the computational difficulties in implementing an optimal receiver in a random-phase case because there is no obvious way of maximizing the log-likelihood function with respect to the data sequences having large sequence lengths.
Georghiades et al. teach that applying the EM algorithm to the fading channel involves calculating the expectation step of the EM algorithm using an initial estimate of the fading âo, vector and using the estimate of the fading vector âo to produce, by maximization, a sequence estimate. The sequence estimate is then used in another equation to produce the next fading estimate, and so on, until convergence. Convergence produces both a sequence estimator and a fading vector estimator.
The expectation (“E”) portion of the EM algorithm includes computing certain values and the maximization (“M”) step provides a convergence to the true ML estimate. In the maximizing step, Georghiades et al. note that their algorithm must maximize by maximizing each individual term in the sum, i.e., by making “symbol-by-symbol decisions.” To improve the efficiency of the algorithm when maximization must be performed on a symbol-by-symbol basis, the Viterbi algorithm is used when trellis coding is present. However, when trellis coding is not present, Georghiades et al. seek to increase efficiency by fixing the number of iterations to two with only “very little performance loss.”
The method described by Georghiades et al. is deficient in several respects. First, it only addresses a single antenna scenario. Further, the approach by Georghiades et al. only addresses re-estimation using all the compensated data symbols for Phase Shift Key (PSK) modulation. In this regard, the approach by Georghiades et al. maintains a high degree of computational complexity that prevents efficient use of the EM algorithm for channel estimation, especially when the number of data symbols in a block or frame is large.
Furthermore, the Georghiades et al. approach is limited to the PSK modulation using a single antenna receiver. Their approach is not well suited to Orthogonal Frequency Division Multiplexing (OFDM), wherein the data-stream is split into multiple RF channels, each of which is sent over a sub-carrier frequency. The S/N ratio of each of the channels in OFDM is precisely defined and is carefully monitored to ensure maximum performance.
Other related patents teach different techniques for channel estimation. For example, U.S. Pat. No. 5,465,276 to Larsson et al., which contents are incorporated herein by reference, teaches a method of adaptive tracking for a fast time-varying channel with no feedback mechanism. The channel estimate taught in the '276 patent uses an estimated time derivative of the channel estimate that is adapted with the aid of the decided symbols. The channel estimate is adapted to the radio channel by the derivate estimate and the decided symbols. The approach of the '276 patent addresses a rapidly varying signal strength and fading where the channel estimate, predicted mainly through the derivative estimate, varies relatively evenly.
The '276 patent is not well suited to the OFDM system where the wireless channel remains quasi-constant over a block of symbols because it would then provide needless derivative computations.
U.S. Pat. No. 5,687,198 to Sexton et al. teaches a method of estimating a channel by first taking an initial channel estimate using pilot symbols and compensating all the data symbols. The '198 patent next teaches taking a group of samples and computing a vector average of the group of samples. Each sample is then compared to the vector average and the largest sample is retained and the others are discarded as noise. After receiving a predetermined number of retained samples, a new channel estimate is generated containing fewer errors than previously would have been obtained if the noisy samples had been retained.
The '198 patent fails to adequately address the deficiencies in the art where all of the data symbols must be compensated for in the first channel estimate, thus increasing the computational complexity of the channel estimation process.